Question

Find the points on the curve y = 2x3 + 3x2 − 12x + 1 where the tangent line is horizontal.

Answer 1

y = 2x³ + 3x² -12x + 1
its tangente is horizontal (tan =0), if it's derivative = 0
y' = 6x² + 6x -12 = 0
Solving this quadratic equation gives :
x= =1 & x = -2
At (1,0) & at (-2,0) tangent is horizontal